LMFDB - Embedded newform 117.3.bd.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(19,117)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	117.28
Dual form			117.3.bd.b.46.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.133975i) q^{2} +(-3.23205 - 1.86603i) q^{4} +(2.63397 - 2.63397i) q^{5} +(5.73205 - 1.53590i) q^{7} +(-2.83013 - 2.83013i) q^{8} +(1.66987 - 0.964102i) q^{10} +(4.19615 - 15.6603i) q^{11} +(-6.50000 - 11.2583i) q^{13} +3.07180 q^{14} +(6.42820 + 11.1340i) q^{16} +(15.9904 + 9.23205i) q^{17} +(1.63397 + 6.09808i) q^{19} +(-13.4282 + 3.59808i) q^{20} +(4.19615 - 7.26795i) q^{22} +(-17.4904 + 10.0981i) q^{23} +11.1244i q^{25} +(-1.74167 - 6.50000i) q^{26} +(-21.3923 - 5.73205i) q^{28} +(4.69615 + 8.13397i) q^{29} +(-11.9282 + 11.9282i) q^{31} +(5.86603 + 21.8923i) q^{32} +(6.75833 + 6.75833i) q^{34} +(11.0526 - 19.1436i) q^{35} +(8.11474 - 30.2846i) q^{37} +3.26795i q^{38} -14.9090 q^{40} +(-44.9186 - 12.0359i) q^{41} +(45.0000 + 25.9808i) q^{43} +(-42.7846 + 42.7846i) q^{44} +(-10.0981 + 2.70577i) q^{46} +(34.3205 + 34.3205i) q^{47} +(-11.9378 + 6.89230i) q^{49} +(-1.49038 + 5.56218i) q^{50} +48.5167i q^{52} +14.7654 q^{53} +(-30.1962 - 52.3013i) q^{55} +(-20.5692 - 11.8756i) q^{56} +(1.25833 + 4.69615i) q^{58} +(92.9615 - 24.9090i) q^{59} +(-12.8135 + 22.1936i) q^{61} +(-7.56218 + 4.36603i) q^{62} -39.6936i q^{64} +(-46.7750 - 12.5333i) q^{65} +(39.0263 + 10.4571i) q^{67} +(-34.4545 - 59.6769i) q^{68} +(8.09103 - 8.09103i) q^{70} +(11.9737 + 44.6865i) q^{71} +(-19.2750 - 19.2750i) q^{73} +(8.11474 - 14.0551i) q^{74} +(6.09808 - 22.7583i) q^{76} -96.2102i q^{77} +62.7461 q^{79} +(46.2583 + 12.3949i) q^{80} +(-20.8468 - 12.0359i) q^{82} +(24.4833 - 24.4833i) q^{83} +(66.4352 - 17.8013i) q^{85} +(19.0192 + 19.0192i) q^{86} +(-56.1962 + 32.4449i) q^{88} +(23.1699 - 86.4711i) q^{89} +(-54.5500 - 54.5500i) q^{91} +75.3731 q^{92} +(12.5622 + 21.7583i) q^{94} +(20.3660 + 11.7583i) q^{95} +(14.1891 + 52.9545i) q^{97} +(-6.89230 + 1.84679i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{4} + 14 q^{5} + 16 q^{7} + 6 q^{8} + 24 q^{10} - 4 q^{11} - 26 q^{13} + 40 q^{14} - 2 q^{16} + 12 q^{17} + 10 q^{19} - 26 q^{20} - 4 q^{22} - 18 q^{23} - 52 q^{26} - 44 q^{28} - 2 q^{29}+ \cdots + 14 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^4 + 14 * q^5 + 16 * q^7 + 6 * q^8 + 24 * q^10 - 4 * q^11 - 26 * q^13 + 40 * q^14 - 2 * q^16 + 12 * q^17 + 10 * q^19 - 26 * q^20 - 4 * q^22 - 18 * q^23 - 52 * q^26 - 44 * q^28 - 2 * q^29 - 20 * q^31 + 20 * q^32 - 18 * q^34 - 32 * q^35 - 68 * q^37 + 72 * q^40 - 100 * q^41 + 180 * q^43 - 88 * q^44 - 30 * q^46 + 68 * q^47 - 72 * q^49 + 46 * q^50 - 128 * q^53 - 100 * q^55 + 84 * q^56 - 40 * q^58 + 164 * q^59 - 124 * q^61 - 6 * q^62 - 52 * q^65 + 118 * q^67 - 72 * q^68 + 164 * q^70 + 86 * q^71 + 58 * q^73 - 68 * q^74 + 14 * q^76 - 40 * q^79 + 140 * q^80 + 24 * q^82 + 188 * q^83 + 96 * q^85 + 180 * q^86 - 204 * q^88 + 110 * q^89 + 52 * q^91 + 156 * q^92 + 26 * q^94 + 78 * q^95 + 178 * q^97 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.133975i	0.250000	+	0.0669873i	0.381643	−	0.924310i	$-0.375358\pi$
$2$	0.500000	+	0.133975i	0.250000	+	0.0669873i	−0.131643	+	0.991297i	$0.542025\pi$
$3$		0			0
$3$		0			0
$4$	−3.23205	−	1.86603i	−0.808013	−	0.466506i
$5$	2.63397	−	2.63397i	0.526795	−	0.526795i	−0.392820	−	0.919615i	$-0.628501\pi$
$5$	2.63397	−	2.63397i	0.526795	−	0.526795i	0.919615	+	0.392820i	$0.128501\pi$
$6$		0			0
$7$	5.73205	−	1.53590i	0.818864	−	0.219414i	0.175014	−	0.984566i	$-0.444003\pi$
$7$	5.73205	−	1.53590i	0.818864	−	0.219414i	0.643850	+	0.765152i	$0.277336\pi$
$8$	−2.83013	−	2.83013i	−0.353766	−	0.353766i
$9$		0			0
$10$	1.66987	−	0.964102i	0.166987	−	0.0964102i
$11$	4.19615	−	15.6603i	0.381468	−	1.42366i	−0.462191	−	0.886780i	$-0.652937\pi$
$11$	4.19615	−	15.6603i	0.381468	−	1.42366i	0.843659	−	0.536879i	$-0.180397\pi$
$12$		0			0
$13$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$13$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$14$	3.07180			0.219414
$15$		0			0
$16$	6.42820	+	11.1340i	0.401763	+	0.695873i
$17$	15.9904	+	9.23205i	0.940611	+	0.543062i	0.890152	−	0.455664i	$-0.150598\pi$
$17$	15.9904	+	9.23205i	0.940611	+	0.543062i	0.0504590	+	0.998726i	$0.483932\pi$
$18$		0			0
$19$	1.63397	+	6.09808i	0.0859987	+	0.320951i	0.995501	−	0.0947465i	$-0.0302040\pi$
$19$	1.63397	+	6.09808i	0.0859987	+	0.320951i	−0.909503	+	0.415698i	$0.863537\pi$
$20$	−13.4282	+	3.59808i	−0.671410	+	0.179904i
$21$		0			0
$22$	4.19615	−	7.26795i	0.190734	−	0.330361i
$23$	−17.4904	+	10.0981i	−0.760451	+	0.439047i	−0.829458	−	0.558569i	$-0.811350\pi$
$23$	−17.4904	+	10.0981i	−0.760451	+	0.439047i	0.0690064	+	0.997616i	$0.478017\pi$
$24$		0			0
$25$			11.1244i			0.444974i
$26$	−1.74167	−	6.50000i	−0.0669873	−	0.250000i
$27$		0			0
$28$	−21.3923	−	5.73205i	−0.764011	−	0.204716i
$29$	4.69615	+	8.13397i	0.161936	+	0.280482i	0.935563	−	0.353160i	$-0.114893\pi$
$29$	4.69615	+	8.13397i	0.161936	+	0.280482i	−0.773627	+	0.633642i	$0.781559\pi$
$30$		0			0
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	−0.872821	−	0.488040i	$-0.837712\pi$
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	0.488040	+	0.872821i	$0.337712\pi$
$32$	5.86603	+	21.8923i	0.183313	+	0.684135i
$33$		0			0
$34$	6.75833	+	6.75833i	0.198774	+	0.198774i
$35$	11.0526	−	19.1436i	0.315787	−	0.546960i
$36$		0			0
$37$	8.11474	−	30.2846i	0.219317	−	0.818503i	−0.765285	−	0.643692i	$-0.777402\pi$
$37$	8.11474	−	30.2846i	0.219317	−	0.818503i	0.984602	−	0.174811i	$-0.0559315\pi$
$38$			3.26795i			0.0859987i
$39$		0			0
$40$	−14.9090			−0.372724
$41$	−44.9186	−	12.0359i	−1.09558	−	0.293558i	−0.334614	−	0.942355i	$-0.608606\pi$
$41$	−44.9186	−	12.0359i	−1.09558	−	0.293558i	−0.760962	+	0.648797i	$0.775272\pi$
$42$		0			0
$43$	45.0000	+	25.9808i	1.04651	+	0.604204i	0.921671	−	0.387973i	$-0.126825\pi$
$43$	45.0000	+	25.9808i	1.04651	+	0.604204i	0.124841	+	0.992177i	$0.460158\pi$
$44$	−42.7846	+	42.7846i	−0.972377	+	0.972377i
$45$		0			0
$46$	−10.0981	+	2.70577i	−0.219523	+	0.0588211i
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	0.970664	−	0.240440i	$-0.0772918\pi$
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	−0.240440	+	0.970664i	$0.577292\pi$
$48$		0			0
$49$	−11.9378	+	6.89230i	−0.243629	+	0.140659i
$50$	−1.49038	+	5.56218i	−0.0298076	+	0.111244i
$51$		0			0
$52$			48.5167i			0.933013i
$53$	14.7654			0.278592			0.139296	−	0.990251i	$-0.455516\pi$
$53$	14.7654			0.278592			0.139296	+	0.990251i	$0.455516\pi$
$54$		0			0
$55$	−30.1962	−	52.3013i	−0.549021	−	0.950932i
$56$	−20.5692	−	11.8756i	−0.367307	−	0.212065i
$57$		0			0
$58$	1.25833	+	4.69615i	0.0216953	+	0.0809681i
$59$	92.9615	−	24.9090i	1.57562	−	0.422186i	0.638053	−	0.769993i	$-0.279740\pi$
$59$	92.9615	−	24.9090i	1.57562	−	0.422186i	0.937566	+	0.347807i	$0.113073\pi$
$60$		0			0
$61$	−12.8135	+	22.1936i	−0.210057	+	0.363829i	−0.951732	−	0.306930i	$-0.900698\pi$
$61$	−12.8135	+	22.1936i	−0.210057	+	0.363829i	0.741675	+	0.670759i	$0.234032\pi$
$62$	−7.56218	+	4.36603i	−0.121971	+	0.0704198i
$63$		0			0
$64$		−	39.6936i		−	0.620212i
$65$	−46.7750	−	12.5333i	−0.719615	−	0.192820i
$66$		0			0
$67$	39.0263	+	10.4571i	0.582482	+	0.156076i	0.538015	−	0.842935i	$-0.319174\pi$
$67$	39.0263	+	10.4571i	0.582482	+	0.156076i	0.0444669	+	0.999011i	$0.485841\pi$
$68$	−34.4545	−	59.6769i	−0.506684	−	0.877602i
$69$		0			0
$70$	8.09103	−	8.09103i	0.115586	−	0.115586i
$71$	11.9737	+	44.6865i	0.168644	+	0.629388i	0.997547	+	0.0699959i	$0.0222986\pi$
$71$	11.9737	+	44.6865i	0.168644	+	0.629388i	−0.828903	+	0.559392i	$0.811035\pi$
$72$		0			0
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	0.562653	−	0.826693i	$-0.309781\pi$
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	−0.826693	+	0.562653i	$0.809781\pi$
$74$	8.11474	−	14.0551i	0.109659	−	0.189934i
$75$		0			0
$76$	6.09808	−	22.7583i	0.0802378	−	0.299452i
$77$		−	96.2102i		−	1.24948i
$78$		0			0
$79$	62.7461			0.794255			0.397127	−	0.917763i	$-0.370007\pi$
$79$	62.7461			0.794255			0.397127	+	0.917763i	$0.370007\pi$
$80$	46.2583	+	12.3949i	0.578229	+	0.154936i
$81$		0			0
$82$	−20.8468	−	12.0359i	−0.254229	−	0.146779i
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	−0.544064	−	0.839044i	$-0.683115\pi$
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	0.839044	+	0.544064i	$0.183115\pi$
$84$		0			0
$85$	66.4352	−	17.8013i	0.781591	−	0.209427i
$86$	19.0192	+	19.0192i	0.221154	+	0.221154i
$87$		0			0
$88$	−56.1962	+	32.4449i	−0.638593	+	0.368692i
$89$	23.1699	−	86.4711i	0.260336	−	0.971586i	−0.704708	−	0.709497i	$-0.748922\pi$
$89$	23.1699	−	86.4711i	0.260336	−	0.971586i	0.965044	−	0.262089i	$-0.0844113\pi$
$90$		0			0
$91$	−54.5500	−	54.5500i	−0.599450	−	0.599450i
$92$	75.3731			0.819272
$93$		0			0
$94$	12.5622	+	21.7583i	0.133640	+	0.231472i
$95$	20.3660	+	11.7583i	0.214379	+	0.123772i
$96$		0			0
$97$	14.1891	+	52.9545i	0.146279	+	0.545923i	0.999695	+	0.0246915i	$0.00786034\pi$
$97$	14.1891	+	52.9545i	0.146279	+	0.545923i	−0.853416	+	0.521231i	$0.825473\pi$
$98$	−6.89230	+	1.84679i	−0.0703296	+	0.0188448i
$99$		0			0
$100$	20.7583	−	35.9545i	0.207583	−	0.359545i
$101$	−138.560	+	79.9974i	−1.37188	+	0.792054i	−0.991164	−	0.132640i	$-0.957655\pi$
$101$	−138.560	+	79.9974i	−1.37188	+	0.792054i	−0.380713	+	0.924693i	$0.624321\pi$
$102$		0			0
$103$		−	78.7705i		−	0.764762i	−0.924005	−	0.382381i	$-0.875104\pi$
$103$		−	78.7705i		−	0.764762i	0.924005	−	0.382381i	$-0.124896\pi$
$104$	−13.4667	+	50.2583i	−0.129487	+	0.483253i
$105$		0			0
$106$	7.38269	+	1.97818i	0.0696480	+	0.0186621i
$107$	−47.6673	−	82.5622i	−0.445489	−	0.771609i	0.552597	−	0.833448i	$-0.313637\pi$
$107$	−47.6673	−	82.5622i	−0.445489	−	0.771609i	−0.998086	+	0.0618392i	$0.980303\pi$
$108$		0			0
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	−0.904135	−	0.427247i	$-0.859483\pi$
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	0.427247	+	0.904135i	$0.359483\pi$
$110$	−8.09103	−	30.1962i	−0.0735549	−	0.274510i
$111$		0			0
$112$	53.9474	+	53.9474i	0.481674	+	0.481674i
$113$	−71.9904	+	124.691i	−0.637083	+	1.10346i	0.348987	+	0.937128i	$0.386526\pi$
$113$	−71.9904	+	124.691i	−0.637083	+	1.10346i	−0.986070	+	0.166332i	$0.946808\pi$
$114$		0			0
$115$	−19.4711	+	72.6673i	−0.169314	+	0.631890i
$116$		−	35.0526i		−	0.302177i
$117$		0			0
$118$	49.8179			0.422186
$119$	105.837	+	28.3590i	0.889388	+	0.238311i
$120$		0			0
$121$	−122.847	−	70.9256i	−1.01526	−	0.586162i
$122$	−9.38011	+	9.38011i	−0.0768861	+	0.0768861i
$123$		0			0
$124$	60.8109	−	16.2942i	0.490410	−	0.131405i
$125$	95.1506	+	95.1506i	0.761205	+	0.761205i
$126$		0			0
$127$	−24.6673	+	14.2417i	−0.194231	+	0.112139i	−0.593962	−	0.804493i	$-0.702437\pi$
$127$	−24.6673	+	14.2417i	−0.194231	+	0.112139i	0.399731	+	0.916633i	$0.369104\pi$
$128$	28.7820	−	107.416i	0.224860	−	0.839188i
$129$		0			0
$130$	−21.7083	−	12.5333i	−0.166987	−	0.0964102i
$131$	2.98076			0.0227539			0.0113770	−	0.999935i	$-0.496379\pi$
$131$	2.98076			0.0227539			0.0113770	+	0.999935i	$0.496379\pi$
$132$		0			0
$133$	18.7321	+	32.4449i	0.140842	+	0.243946i
$134$	18.1122	+	10.4571i	0.135165	+	0.0780378i
$135$		0			0
$136$	−19.1269	−	71.3827i	−0.140639	−	0.524873i
$137$	−94.6051	+	25.3494i	−0.690548	+	0.185032i	−0.586993	−	0.809592i	$-0.699688\pi$
$137$	−94.6051	+	25.3494i	−0.690548	+	0.185032i	−0.103555	+	0.994624i	$0.533022\pi$
$138$		0			0
$139$	−16.2154	+	28.0859i	−0.116657	+	0.202057i	−0.918441	−	0.395558i	$-0.870551\pi$
$139$	−16.2154	+	28.0859i	−0.116657	+	0.202057i	0.801784	+	0.597614i	$0.203885\pi$
$140$	−71.4449	+	41.2487i	−0.510320	+	0.294634i
$141$		0			0
$142$			23.9474i			0.168644i
$143$	−203.583	+	54.5500i	−1.42366	+	0.381468i
$144$		0			0
$145$	33.7942	+	9.05514i	0.233064	+	0.0624492i
$146$	−7.05514	−	12.2199i	−0.0483229	−	0.0836976i
$147$		0			0
$148$	−82.7391	+	82.7391i	−0.559048	+	0.559048i
$149$	33.0903	+	123.495i	0.222083	+	0.828824i	0.983552	+	0.180624i	$0.0578116\pi$
$149$	33.0903	+	123.495i	0.222083	+	0.828824i	−0.761469	+	0.648201i	$0.775522\pi$
$150$		0			0
$151$	127.995	+	127.995i	0.847648	+	0.847648i	0.989839	−	0.142191i	$-0.0454148\pi$
$151$	127.995	+	127.995i	0.847648	+	0.847648i	−0.142191	+	0.989839i	$0.545415\pi$
$152$	12.6340	−	21.8827i	0.0831183	−	0.143965i
$153$		0			0
$154$	12.8897	−	48.1051i	0.0836995	−	0.312371i
$155$			62.8372i			0.405401i
$156$		0			0
$157$	−97.7461			−0.622587			−0.311293	−	0.950314i	$-0.600762\pi$
$157$	−97.7461			−0.622587			−0.311293	+	0.950314i	$0.600762\pi$
$158$	31.3731	+	8.40639i	0.198564	+	0.0532050i
$159$		0			0
$160$	73.1147	+	42.2128i	0.456967	+	0.263830i
$161$	−84.7461	+	84.7461i	−0.526374	+	0.526374i
$162$		0			0
$163$	−122.282	+	32.7654i	−0.750197	+	0.201015i	−0.613605	−	0.789613i	$-0.710281\pi$
$163$	−122.282	+	32.7654i	−0.750197	+	0.201015i	−0.136591	+	0.990627i	$0.543615\pi$
$164$	122.720	+	122.720i	0.748292	+	0.748292i
$165$		0			0
$166$	15.5218	−	8.96152i	0.0935049	−	0.0539851i
$167$	13.5936	−	50.7321i	0.0813989	−	0.303785i	−0.913209	−	0.407491i	$-0.866404\pi$
$167$	13.5936	−	50.7321i	0.0813989	−	0.303785i	0.994608	+	0.103707i	$0.0330703\pi$
$168$		0			0
$169$	−84.5000	+	146.358i	−0.500000	+	0.866025i
$170$	35.6025			0.209427
$171$		0			0
$172$	−96.9615	−	167.942i	−0.563730	−	0.976409i
$173$	−118.865	−	68.6269i	−0.687083	−	0.396687i	0.115435	−	0.993315i	$-0.463174\pi$
$173$	−118.865	−	68.6269i	−0.687083	−	0.396687i	−0.802518	+	0.596628i	$0.796507\pi$
$174$		0			0
$175$	17.0859	+	63.7654i	0.0976336	+	0.364374i
$176$	201.335	−	53.9474i	1.14395	−	0.306520i
$177$		0			0
$178$	23.1699	−	40.1314i	0.130168	−	0.225457i
$179$	−0.903811	+	0.521815i	−0.00504922	+	0.00291517i	−0.502522	−	0.864564i	$-0.667595\pi$
$179$	−0.903811	+	0.521815i	−0.00504922	+	0.00291517i	0.497473	+	0.867479i	$0.334261\pi$
$180$		0			0
$181$		−	23.0807i		−	0.127518i	−0.997965	−	0.0637589i	$-0.979691\pi$
$181$		−	23.0807i		−	0.127518i	0.997965	−	0.0637589i	$-0.0203089\pi$
$182$	−19.9667	−	34.5833i	−0.109707	−	0.190018i
$183$		0			0
$184$	78.0788	+	20.9212i	0.424342	+	0.113702i
$185$	−58.3949	−	101.143i	−0.315648	−	0.546718i
$186$		0			0
$187$	211.674	−	211.674i	1.13195	−	1.13195i
$188$	−46.8827	−	174.969i	−0.249376	−	0.930684i
$189$		0			0
$190$	8.60770	+	8.60770i	0.0453037	+	0.0453037i
$191$	147.002	−	254.615i	0.769643	−	1.33306i	−0.168113	−	0.985768i	$-0.553767\pi$
$191$	147.002	−	254.615i	0.769643	−	1.33306i	0.937756	−	0.347294i	$-0.112899\pi$
$192$		0			0
$193$	85.5507	−	319.279i	0.443268	−	1.65430i	−0.277202	−	0.960812i	$-0.589407\pi$
$193$	85.5507	−	319.279i	0.443268	−	1.65430i	0.720470	−	0.693486i	$-0.243926\pi$
$194$			28.3782i			0.146279i
$195$		0			0
$196$	51.4449			0.262474
$197$	−85.1122	−	22.8057i	−0.432041	−	0.115765i	0.0362429	−	0.999343i	$-0.488461\pi$
$197$	−85.1122	−	22.8057i	−0.432041	−	0.115765i	−0.468284	+	0.883578i	$0.655128\pi$
$198$		0			0
$199$	174.452	+	100.720i	0.876643	+	0.506130i	0.869550	−	0.493845i	$-0.164409\pi$
$199$	174.452	+	100.720i	0.876643	+	0.506130i	0.00709275	+	0.999975i	$0.497742\pi$
$200$	31.4833	−	31.4833i	0.157417	−	0.157417i
$201$		0			0
$202$	−79.9974	+	21.4352i	−0.396027	+	0.106115i
$203$	39.4115	+	39.4115i	0.194146	+	0.194146i
$204$		0			0
$205$	−150.017	+	86.6122i	−0.731789	+	0.422498i
$206$	10.5532	−	39.3853i	0.0512294	−	0.191191i
$207$		0			0
$208$	83.5666	−	144.742i	0.401763	−	0.695873i
$209$	102.354			0.489731
$210$		0			0
$211$	−36.6481	−	63.4763i	−0.173687	−	0.300836i	0.766019	−	0.642818i	$-0.222235\pi$
$211$	−36.6481	−	63.4763i	−0.173687	−	0.300836i	−0.939706	+	0.341983i	$0.888902\pi$
$212$	−47.7224	−	27.5526i	−0.225106	−	0.129965i
$213$		0			0
$214$	−12.7724	−	47.6673i	−0.0596842	−	0.222744i
$215$	186.962	−	50.0962i	0.869588	−	0.233006i
$216$		0			0
$217$	−50.0526	+	86.6936i	−0.230657	+	0.399510i
$218$	−32.9545	+	19.0263i	−0.151167	+	0.0872765i
$219$		0			0
$220$			225.387i			1.02449i
$221$		−	240.033i		−	1.08612i
$222$		0			0
$223$	−367.533	−	98.4801i	−1.64813	−	0.441615i	−0.689040	−	0.724723i	$-0.741968\pi$
$223$	−367.533	−	98.4801i	−1.64813	−	0.441615i	−0.959088	+	0.283108i	$0.908634\pi$
$224$	67.2487	+	116.478i	0.300217	+	0.519992i
$225$		0			0
$226$	−52.7006	+	52.7006i	−0.233189	+	0.233189i
$227$	108.280	+	404.107i	0.477005	+	1.78021i	0.613640	+	0.789586i	$0.289704\pi$
$227$	108.280	+	404.107i	0.477005	+	1.78021i	−0.136635	+	0.990621i	$0.543629\pi$
$228$		0			0
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	0.531486	−	0.847067i	$-0.321634\pi$
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	−0.847067	+	0.531486i	$0.821634\pi$
$230$	−19.4711	+	33.7250i	−0.0846571	+	0.146630i
$231$		0			0
$232$	9.72947	−	36.3109i	0.0419374	−	0.156512i
$233$		−	256.592i		−	1.10125i	−0.834751	−	0.550627i	$-0.814389\pi$
$233$		−	256.592i		−	1.10125i	0.834751	−	0.550627i	$-0.185611\pi$
$234$		0			0
$235$	180.799			0.769356
$236$	−346.937	−	92.9615i	−1.47007	−	0.393905i
$237$		0			0
$238$	49.1192	+	28.3590i	0.206383	+	0.119155i
$239$	−39.3449	+	39.3449i	−0.164623	+	0.164623i	−0.784611	−	0.619988i	$-0.787137\pi$
$239$	−39.3449	+	39.3449i	−0.164623	+	0.164623i	0.619988	+	0.784611i	$0.287137\pi$
$240$		0			0
$241$	233.351	−	62.5263i	0.968262	−	0.259445i	0.260168	−	0.965563i	$-0.416222\pi$
$241$	233.351	−	62.5263i	0.968262	−	0.259445i	0.708094	+	0.706118i	$0.249555\pi$
$242$	−51.9212	−	51.9212i	−0.214550	−	0.214550i
$243$		0			0
$244$	82.8275	−	47.8205i	0.339457	−	0.195986i
$245$	−13.2898	+	49.5981i	−0.0542439	+	0.202441i
$246$		0			0
$247$	58.0333	−	58.0333i	0.234953	−	0.234953i
$248$	67.5167			0.272245
$249$		0			0
$250$	34.8275	+	60.3231i	0.139310	+	0.241292i
$251$	221.375	+	127.811i	0.881972	+	0.509207i	0.871308	−	0.490736i	$-0.163272\pi$
$251$	221.375	+	127.811i	0.881972	+	0.509207i	0.0106638	+	0.999943i	$0.496606\pi$
$252$		0			0
$253$	84.7461	+	316.277i	0.334965	+	1.25011i
$254$	−14.2417	+	3.81604i	−0.0560696	+	0.0150238i
$255$		0			0
$256$	−50.6051	+	87.6506i	−0.197676	+	0.342385i
$257$	−85.7731	+	49.5211i	−0.333747	+	0.192689i	−0.657504	−	0.753451i	$-0.728388\pi$
$257$	−85.7731	+	49.5211i	−0.333747	+	0.192689i	0.323756	+	0.946141i	$0.395054\pi$
$258$		0			0
$259$		−	186.056i		−	0.718364i
$260$	127.792	+	127.792i	0.491506	+	0.491506i
$261$		0			0
$262$	1.49038	+	0.399346i	0.00568848	+	0.00152422i
$263$	−127.669	−	221.130i	−0.485434	−	0.840797i	0.514426	−	0.857535i	$-0.328005\pi$
$263$	−127.669	−	221.130i	−0.485434	−	0.840797i	−0.999860	+	0.0167383i	$0.994672\pi$
$264$		0			0
$265$	38.8916	−	38.8916i	0.146761	−	0.146761i
$266$	5.01924	+	18.7321i	0.0188693	+	0.0704212i
$267$		0			0
$268$	−106.622	−	106.622i	−0.397842	−	0.397842i
$269$	−46.3538	+	80.2872i	−0.172319	+	0.298465i	−0.939230	−	0.343288i	$-0.888459\pi$
$269$	−46.3538	+	80.2872i	−0.172319	+	0.298465i	0.766911	+	0.641753i	$0.221793\pi$
$270$		0			0
$271$	−113.133	+	422.219i	−0.417466	+	1.55800i	0.362379	+	0.932031i	$0.381965\pi$
$271$	−113.133	+	422.219i	−0.417466	+	1.55800i	−0.779845	+	0.625973i	$0.784702\pi$
$272$			237.382i			0.872728i
$273$		0			0
$274$	−50.6987			−0.185032
$275$	174.210	+	46.6795i	0.633492	+	0.169744i
$276$		0			0
$277$	−302.110	−	174.423i	−1.09065	−	0.629686i	−0.156899	−	0.987615i	$-0.550150\pi$
$277$	−302.110	−	174.423i	−1.09065	−	0.629686i	−0.933749	+	0.357929i	$0.883483\pi$
$278$	−11.8705	+	11.8705i	−0.0426996	+	0.0426996i
$279$		0			0
$280$	−85.4589	+	22.8987i	−0.305211	+	0.0817809i
$281$	−91.9737	−	91.9737i	−0.327309	−	0.327309i	0.524254	−	0.851562i	$-0.324344\pi$
$281$	−91.9737	−	91.9737i	−0.327309	−	0.327309i	−0.851562	+	0.524254i	$0.824344\pi$
$282$		0			0
$283$	−30.8038	+	17.7846i	−0.108848	+	0.0628431i	−0.553435	−	0.832892i	$-0.686683\pi$
$283$	−30.8038	+	17.7846i	−0.108848	+	0.0628431i	0.444588	+	0.895735i	$0.353350\pi$
$284$	44.6865	−	166.772i	0.157347	−	0.587227i
$285$		0			0
$286$	−109.100			−0.381468
$287$	−275.962			−0.961538
$288$		0			0
$289$	25.9615	+	44.9667i	0.0898323	+	0.155594i
$290$	15.6840	+	9.05514i	0.0540826	+	0.0312246i
$291$		0			0
$292$	26.3301	+	98.2654i	0.0901717	+	0.336525i
$293$	−386.758	+	103.631i	−1.31999	+	0.353691i	−0.848975	−	0.528433i	$-0.822780\pi$
$293$	−386.758	+	103.631i	−1.31999	+	0.353691i	−0.471017	+	0.882124i	$0.656113\pi$
$294$		0			0
$295$	179.249	−	310.468i	0.607623	−	1.05243i
$296$	−108.675	+	62.7436i	−0.367145	+	0.211971i
$297$		0			0
$298$			66.1807i			0.222083i
$299$	227.375	+	131.275i	0.760451	+	0.439047i
$300$		0			0
$301$	297.846	+	79.8076i	0.989522	+	0.265142i
$302$	46.8494	+	81.1455i	0.155130	+	0.268694i
$303$		0			0
$304$	−57.3923	+	57.3923i	−0.188790	+	0.188790i
$305$	24.7070	+	92.2077i	0.0810065	+	0.302320i
$306$		0			0
$307$	260.219	+	260.219i	0.847619	+	0.847619i	0.989836	−	0.142216i	$-0.0454228\pi$
$307$	260.219	+	260.219i	0.847619	+	0.847619i	−0.142216	+	0.989836i	$0.545423\pi$
$308$	−179.531	+	310.956i	−0.582892	+	1.00960i
$309$		0			0
$310$	−8.41858	+	31.4186i	−0.0271567	+	0.101350i
$311$			71.4782i			0.229833i	0.993375	+	0.114917i	$0.0366601\pi$
$311$			71.4782i			0.229833i	−0.993375	+	0.114917i	$0.963340\pi$
$312$		0			0
$313$	−394.315			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$313$	−394.315			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$314$	−48.8731	−	13.0955i	−0.155647	−	0.0417054i
$315$		0			0
$316$	−202.799	−	117.086i	−0.641768	−	0.370525i
$317$	206.054	−	206.054i	0.650014	−	0.650014i	−0.302982	−	0.952996i	$-0.597982\pi$
$317$	206.054	−	206.054i	0.650014	−	0.650014i	0.952996	+	0.302982i	$0.0979823\pi$
$318$		0			0
$319$	147.086	−	39.4115i	0.461084	−	0.123547i
$320$	−104.552	−	104.552i	−0.326725	−	0.326725i
$321$		0			0
$322$	−53.7269	+	31.0192i	−0.166854	+	0.0963330i
$323$	−30.1699	+	112.595i	−0.0934052	+	0.348593i
$324$		0			0
$325$	125.242	−	72.3083i	0.385359	−	0.222487i
$326$	−65.5307			−0.201015
$327$		0			0
$328$	93.0622	+	161.188i	0.283726	+	0.491428i
$329$	249.440	+	144.014i	0.758175	+	0.437733i
$330$		0			0
$331$	−119.397	−	445.597i	−0.360717	−	1.34622i	−0.873135	−	0.487479i	$-0.837917\pi$
$331$	−119.397	−	445.597i	−0.360717	−	1.34622i	0.512417	−	0.858737i	$-0.328750\pi$
$332$	−124.818	+	33.4449i	−0.375958	+	0.100738i
$333$		0			0
$334$	13.5936	−	23.5448i	0.0406994	−	0.0704935i
$335$	130.338	−	75.2506i	0.389068	−	0.224629i
$336$		0			0
$337$			144.779i			0.429613i	0.976657	+	0.214806i	$0.0689120\pi$
$337$			144.779i			0.429613i	−0.976657	+	0.214806i	$0.931088\pi$
$338$	−61.8583	+	61.8583i	−0.183013	+	0.183013i
$339$		0			0
$340$	−247.940	−	66.4352i	−0.729234	−	0.195398i
$341$	136.746	+	236.851i	0.401015	+	0.694578i
$342$		0			0
$343$	−263.454	+	263.454i	−0.768087	+	0.768087i
$344$	−53.8269	−	200.885i	−0.156473	−	0.583967i
$345$		0			0
$346$	−50.2384	−	50.2384i	−0.145198	−	0.145198i
$347$	243.590	−	421.911i	0.701989	−	1.21588i	−0.265778	−	0.964034i	$-0.585629\pi$
$347$	243.590	−	421.911i	0.701989	−	1.21588i	0.967767	−	0.251847i	$-0.0810380\pi$
$348$		0			0
$349$	−3.04036	+	11.3468i	−0.00871164	+	0.0325123i	−0.970145	−	0.242526i	$-0.922024\pi$
$349$	−3.04036	+	11.3468i	−0.00871164	+	0.0325123i	0.961433	+	0.275039i	$0.0886906\pi$
$350$			34.1718i			0.0976336i
$351$		0			0
$352$	367.454			1.04390
$353$	276.169	+	73.9993i	0.782349	+	0.209630i	0.627820	−	0.778358i	$-0.283947\pi$
$353$	276.169	+	73.9993i	0.782349	+	0.209630i	0.154529	+	0.987988i	$0.450614\pi$
$354$		0			0
$355$	149.242	+	86.1647i	0.420399	+	0.242718i
$356$	−236.244	+	236.244i	−0.663605	+	0.663605i
$357$		0			0
$358$	−0.521815	+	0.139820i	−0.00145758	+	0.000390559i
$359$	−92.0770	−	92.0770i	−0.256482	−	0.256482i	0.567140	−	0.823622i	$-0.308050\pi$
$359$	−92.0770	−	92.0770i	−0.256482	−	0.256482i	−0.823622	+	0.567140i	$0.808050\pi$
$360$		0			0
$361$	278.119	−	160.572i	0.770411	−	0.444797i
$362$	3.09223	−	11.5404i	0.00854207	−	0.0318795i
$363$		0			0
$364$	74.5167	+	278.100i	0.204716	+	0.764011i
$365$	−101.540			−0.278191
$366$		0			0
$367$	−6.27499	−	10.8686i	−0.0170981	−	0.0296147i	0.857350	−	0.514734i	$-0.172109\pi$
$367$	−6.27499	−	10.8686i	−0.0170981	−	0.0296147i	−0.874448	+	0.485120i	$0.838776\pi$
$368$	−224.863	−	129.825i	−0.611042	−	0.352785i
$369$		0			0
$370$	−15.6469	−	58.3949i	−0.0422888	−	0.157824i
$371$	84.6359	−	22.6781i	0.228129	−	0.0611270i
$372$		0			0
$373$	155.638	−	269.574i	0.417261	−	0.722718i	−0.578402	−	0.815752i	$-0.696323\pi$
$373$	155.638	−	269.574i	0.417261	−	0.722718i	0.995663	+	0.0930345i	$0.0296567\pi$
$374$	134.196	−	77.4782i	0.358813	−	0.207161i
$375$		0			0
$376$		−	194.263i		−	0.516656i
$377$	61.0500	−	105.742i	0.161936	−	0.280482i
$378$		0			0
$379$	379.858	+	101.783i	1.00226	+	0.268556i	0.722394	−	0.691482i	$-0.243042\pi$
$379$	379.858	+	101.783i	1.00226	+	0.268556i	0.279871	+	0.960038i	$0.409708\pi$
$380$	−43.8827	−	76.0070i	−0.115481	−	0.200019i
$381$		0			0
$382$	107.613	−	107.613i	0.281709	−	0.281709i
$383$	−191.061	−	713.051i	−0.498855	−	1.86175i	−0.507269	−	0.861788i	$-0.669345\pi$
$383$	−191.061	−	713.051i	−0.498855	−	1.86175i	0.00841386	−	0.999965i	$-0.497322\pi$
$384$		0			0
$385$	−253.415	−	253.415i	−0.658222	−	0.658222i
$386$	85.5507	−	148.178i	0.221634	−	0.383881i
$387$		0			0
$388$	52.9545	−	197.629i	0.136481	−	0.509353i
$389$		−	344.478i		−	0.885548i	−0.896633	−	0.442774i	$-0.853994\pi$
$389$		−	344.478i		−	0.885548i	0.896633	−	0.442774i	$-0.146006\pi$
$390$		0			0
$391$	−372.904			−0.953718
$392$	53.2917	+	14.2795i	0.135948	+	0.0364272i
$393$		0			0
$394$	−39.5007	−	22.8057i	−0.100256	−	0.0578826i
$395$	165.272	−	165.272i	0.418409	−	0.418409i
$396$		0			0
$397$	−678.422	+	181.783i	−1.70887	+	0.457891i	−0.975148	−	0.221556i	$-0.928886\pi$
$397$	−678.422	+	181.783i	−1.70887	+	0.457891i	−0.733725	+	0.679447i	$0.762220\pi$
$398$	73.7321	+	73.7321i	0.185256	+	0.185256i
$399$		0			0
$400$	−123.858	+	71.5096i	−0.309646	+	0.178774i
$401$	−146.833	+	547.989i	−0.366168	+	1.36656i	0.499663	+	0.866220i	$0.333457\pi$
$401$	−146.833	+	547.989i	−0.366168	+	1.36656i	−0.865831	+	0.500336i	$0.833210\pi$
$402$		0			0
$403$	211.825	+	56.7583i	0.525620	+	0.140840i
$404$	597.109			1.47799
$405$		0			0
$406$	14.4256	+	24.9859i	0.0355311	+	0.0615417i
$407$	−440.214	−	254.158i	−1.08161	−	0.624466i
$408$		0			0
$409$	26.3212	+	98.2321i	0.0643550	+	0.240176i	0.990609	−	0.136723i	$-0.0436570\pi$
$409$	26.3212	+	98.2321i	0.0643550	+	0.240176i	−0.926254	+	0.376899i	$0.876990\pi$
$410$	−86.6122	+	23.2077i	−0.211249	+	0.0566040i
$411$		0			0
$412$	−146.988	+	254.590i	−0.356767	+	0.617938i
$413$	494.603	−	285.559i	1.19758	−	0.691426i
$414$		0			0
$415$		−	128.977i		−	0.310788i
$416$	208.342	−	208.342i	0.500821	−	0.500821i
$417$		0			0
$418$	51.1769	+	13.7128i	0.122433	+	0.0328058i
$419$	322.279	+	558.203i	0.769162	+	1.33223i	0.938018	+	0.346587i	$0.112659\pi$
$419$	322.279	+	558.203i	0.769162	+	1.33223i	−0.168856	+	0.985641i	$0.554007\pi$
$420$		0			0
$421$	346.619	−	346.619i	0.823322	−	0.823322i	−0.163261	−	0.986583i	$-0.552201\pi$
$421$	346.619	−	346.619i	0.823322	−	0.823322i	0.986583	+	0.163261i	$0.0522013\pi$
$422$	−9.81982	−	36.6481i	−0.0232697	−	0.0868437i
$423$		0			0
$424$	−41.7879	−	41.7879i	−0.0985563	−	0.0985563i
$425$	−102.701	+	177.883i	−0.241649	+	0.418547i
$426$		0			0
$427$	−39.3604	+	146.895i	−0.0921788	+	0.344016i
$428$			355.794i			0.831293i
$429$		0			0
$430$	100.192			0.233006
$431$	−101.699	−	27.2501i	−0.235960	−	0.0632253i	0.138901	−	0.990306i	$-0.455643\pi$
$431$	−101.699	−	27.2501i	−0.235960	−	0.0632253i	−0.374861	+	0.927081i	$0.622310\pi$
$432$		0			0
$433$	596.892	+	344.616i	1.37850	+	0.795880i	0.991979	−	0.126399i	$-0.0403421\pi$
$433$	596.892	+	344.616i	1.37850	+	0.795880i	0.386525	+	0.922279i	$0.373675\pi$
$434$	−36.6410	+	36.6410i	−0.0844263	+	0.0844263i
$435$		0			0
$436$	265.002	−	71.0070i	0.607802	−	0.162860i
$437$	−90.1577	−	90.1577i	−0.206310	−	0.206310i
$438$		0			0
$439$	78.0577	−	45.0666i	0.177808	−	0.102657i	−0.408454	−	0.912779i	$-0.633932\pi$
$439$	78.0577	−	45.0666i	0.177808	−	0.102657i	0.586262	+	0.810121i	$0.300599\pi$
$440$	−62.5603	+	233.478i	−0.142182	+	0.530632i
$441$		0			0
$442$	32.1584	−	120.017i	0.0727565	−	0.271531i
$443$	−642.277			−1.44983			−0.724917	−	0.688836i	$-0.758122\pi$
$443$	−642.277			−1.44983			−0.724917	+	0.688836i	$0.758122\pi$
$444$		0			0
$445$	−166.734	−	288.792i	−0.374683	−	0.648970i
$446$	−170.572	−	98.4801i	−0.382450	−	0.220807i
$447$		0			0
$448$	−60.9653	−	227.526i	−0.136083	−	0.507870i
$449$	−22.6007	+	6.05583i	−0.0503355	+	0.0134874i	−0.283899	−	0.958854i	$-0.591628\pi$
$449$	−22.6007	+	6.05583i	−0.0503355	+	0.0134874i	0.233563	+	0.972342i	$0.424961\pi$
$450$		0			0
$451$	−376.970	+	652.932i	−0.835855	+	1.44774i
$452$	465.353	−	268.672i	1.02954	−	0.594407i
$453$		0			0
$454$			216.560i			0.477005i
$455$	−287.367			−0.631575
$456$		0			0
$457$	228.698	+	61.2795i	0.500433	+	0.134091i	0.500201	−	0.865909i	$-0.333259\pi$
$457$	228.698	+	61.2795i	0.500433	+	0.134091i	0.000232237		1.00000i	$0.499926\pi$
$458$	−26.4519	−	45.8160i	−0.0577553	−	0.100035i
$459$		0			0
$460$	198.531	−	198.531i	0.431589	−	0.431589i
$461$	12.6032	+	47.0359i	0.0273389	+	0.102030i	0.978247	−	0.207443i	$-0.0665141\pi$
$461$	12.6032	+	47.0359i	0.0273389	+	0.102030i	−0.950908	+	0.309473i	$0.899847\pi$
$462$		0			0
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.990871	−	0.134811i	$-0.956957\pi$
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.134811	−	0.990871i	$-0.543043\pi$
$464$	−60.3756	+	104.574i	−0.130120	+	0.225374i
$465$		0			0
$466$	34.3768	−	128.296i	0.0737700	−	0.275314i
$467$			141.415i			0.302817i	0.988471	+	0.151408i	$0.0483808\pi$
$467$			141.415i			0.302817i	−0.988471	+	0.151408i	$0.951619\pi$
$468$		0			0
$469$	239.762			0.511219
$470$	90.3993	+	24.2224i	0.192339	+	0.0515371i
$471$		0			0
$472$	−333.588	−	192.597i	−0.706755	−	0.408045i
$473$	595.692	−	595.692i	1.25939	−	1.25939i
$474$		0			0
$475$	−67.8372	+	18.1769i	−0.142815	+	0.0382672i
$476$	−289.153	−	289.153i	−0.607463	−	0.607463i
$477$		0			0
$478$	−24.9437	+	14.4012i	−0.0521834	+	0.0301281i
$479$	−193.783	+	723.207i	−0.404557	+	1.50983i	0.400315	+	0.916378i	$0.368901\pi$
$479$	−193.783	+	723.207i	−0.404557	+	1.50983i	−0.804872	+	0.593449i	$0.797766\pi$
$480$		0			0
$481$	−393.700	+	105.492i	−0.818503	+	0.219317i
$482$	125.053			0.259445
$483$		0			0
$484$	264.698	+	458.470i	0.546897	+	0.947253i
$485$	176.855	+	102.107i	0.364648	+	0.210530i
$486$		0			0
$487$	−62.9371	−	234.885i	−0.129234	−	0.482309i	0.870721	−	0.491778i	$-0.163653\pi$
$487$	−62.9371	−	234.885i	−0.129234	−	0.482309i	−0.999955	+	0.00946847i	$0.996986\pi$
$488$	99.0744	−	26.5469i	0.203021	−	0.0543994i
$489$		0			0
$490$	−13.2898	+	23.0185i	−0.0271220	+	0.0469766i
$491$	73.3191	−	42.3308i	0.149326	−	0.0862135i	−0.423475	−	0.905908i	$-0.639190\pi$
$491$	73.3191	−	42.3308i	0.149326	−	0.0862135i	0.572801	+	0.819694i	$0.305857\pi$
$492$		0			0
$493$			173.420i			0.351766i
$494$	36.7917	−	21.2417i	0.0744770	−	0.0429993i
$495$		0			0
$496$	−209.485	−	56.1314i	−0.422349	−	0.113168i
$497$	137.268	+	237.755i	0.276193	+	0.478380i
$498$		0			0
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	−0.828832	−	0.559498i	$-0.810994\pi$
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	0.559498	+	0.828832i	$0.310994\pi$
$500$	−129.978	−	485.085i	−0.259956	−	0.970170i
$501$		0			0
$502$	93.5641	+	93.5641i	0.186383	+	0.186383i
$503$	−398.200	+	689.703i	−0.791650	+	1.37118i	0.133295	+	0.991076i	$0.457444\pi$
$503$	−398.200	+	689.703i	−0.791650	+	1.37118i	−0.924945	+	0.380102i	$0.875889\pi$
$504$		0			0
$505$	−154.251	+	575.674i	−0.305448	+	1.13995i
$506$			169.492i			0.334965i
$507$		0			0
$508$	106.301			0.209254
$509$	−79.6051	−	21.3301i	−0.156395	−	0.0419059i	0.179772	−	0.983708i	$-0.442464\pi$
$509$	−79.6051	−	21.3301i	−0.156395	−	0.0419059i	−0.336167	+	0.941802i	$0.609131\pi$
$510$		0			0
$511$	−140.090	−	80.8808i	−0.274148	−	0.158279i
$512$	−351.581	+	351.581i	−0.686682	+	0.686682i
$513$		0			0
$514$	−49.5211	+	13.2691i	−0.0963446	+	0.0258155i
$515$	−207.480	−	207.480i	−0.402873	−	0.402873i
$516$		0			0
$517$	681.482	−	393.454i	1.31815	−	0.761032i
$518$	24.9268	−	93.0282i	0.0481213	−	0.179591i
$519$		0			0
$520$	96.9083	+	167.850i	0.186362	+	0.322789i
$521$	−677.011			−1.29945			−0.649723	−	0.760171i	$-0.725115\pi$
$521$	−677.011			−1.29945			−0.649723	+	0.760171i	$0.725115\pi$
$522$		0			0
$523$	91.8269	+	159.049i	0.175577	+	0.304109i	0.940361	−	0.340179i	$-0.110488\pi$
$523$	91.8269	+	159.049i	0.175577	+	0.304109i	−0.764784	+	0.644287i	$0.777154\pi$
$524$	−9.63397	−	5.56218i	−0.0183854	−	0.0106148i
$525$		0			0
$526$	−34.2089	−	127.669i	−0.0650358	−	0.242717i
$527$	−300.858	+	80.6147i	−0.570889	+	0.152969i
$528$		0			0
$529$	−60.5577	+	104.889i	−0.114476	+	0.198278i
$530$	24.6563	−	14.2353i	0.0465213	−	0.0268591i
$531$		0			0
$532$		−	139.818i		−	0.262816i
$533$	156.467	+	583.942i	0.293558	+	1.09558i
$534$		0			0
$535$	−343.021	−	91.9122i	−0.641161	−	0.171799i
$536$	−80.8545	−	140.044i	−0.150848	−	0.261276i
$537$		0			0
$538$	−33.9334	+	33.9334i	−0.0630732	+	0.0630732i
$539$	57.8423	+	215.870i	0.107314	+	0.400502i
$540$		0			0
$541$	317.629	+	317.629i	0.587114	+	0.587114i	0.936849	−	0.349735i	$-0.113728\pi$
$541$	317.629	+	317.629i	0.587114	+	0.587114i	−0.349735	+	0.936849i	$0.613728\pi$
$542$	−113.133	+	195.953i	−0.208733	+	0.361536i
$543$		0			0
$544$	−108.311	+	404.222i	−0.199101	+	0.743055i
$545$			273.832i			0.502444i
$546$		0			0
$547$	−724.904			−1.32524			−0.662618	−	0.748958i	$-0.730555\pi$
$547$	−724.904			−1.32524			−0.662618	+	0.748958i	$0.730555\pi$
$548$	353.071	+	94.6051i	0.644290	+	0.172637i
$549$		0			0
$550$	80.8513	+	46.6795i	0.147002	+	0.0848718i
$551$	−41.9282	+	41.9282i	−0.0760947	+	0.0760947i
$552$		0			0
$553$	359.664	−	96.3717i	0.650387	−	0.174271i
$554$	−127.687	−	127.687i	−0.230481	−	0.230481i
$555$		0			0
$556$	104.818	−	60.5167i	0.188521	−	0.108843i
$557$	31.0641	−	115.933i	0.0557703	−	0.208138i	−0.932418	−	0.361381i	$-0.882305\pi$
$557$	31.0641	−	115.933i	0.0557703	−	0.208138i	0.988188	+	0.153244i	$0.0489719\pi$
$558$		0			0
$559$		−	675.500i		−	1.20841i
$560$	284.192			0.507486
$561$		0			0
$562$	−33.6647	−	58.3090i	−0.0599016	−	0.103753i
$563$	534.888	+	308.818i	0.950068	+	0.548522i	0.893102	−	0.449854i	$-0.148524\pi$
$563$	534.888	+	308.818i	0.950068	+	0.548522i	0.0569660	+	0.998376i	$0.481857\pi$
$564$		0			0
$565$	138.812	+	518.054i	0.245685	+	0.916909i
$566$	−17.7846	+	4.76537i	−0.0314216	+	0.00841938i
$567$		0			0
$568$	92.5814	−	160.356i	0.162995	−	0.282316i
$569$	381.315	−	220.153i	0.670150	−	0.386911i	−0.125983	−	0.992032i	$-0.540209\pi$
$569$	381.315	−	220.153i	0.670150	−	0.386911i	0.796133	+	0.605121i	$0.206875\pi$
$570$		0			0
$571$			618.249i			1.08275i	0.840782	+	0.541374i	$0.182096\pi$
$571$			618.249i			1.08275i	−0.840782	+	0.541374i	$0.817904\pi$
$572$	759.783	+	203.583i	1.32829	+	0.355915i
$573$		0			0
$574$	−137.981	−	36.9718i	−0.240385	−	0.0644109i
$575$	−112.335	−	194.569i	−0.195365	−	0.338381i
$576$		0			0
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	−0.899119	−	0.437704i	$-0.855792\pi$
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	0.437704	+	0.899119i	$0.355792\pi$
$578$	6.95637	+	25.9615i	0.0120352	+	0.0449161i
$579$		0			0
$580$	−92.3275	−	92.3275i	−0.159185	−	0.159185i
$581$	102.736	−	177.944i	0.176826	−	0.306271i
$582$		0			0
$583$	61.9578	−	231.229i	0.106274	−	0.396620i
$584$			109.101i			0.186817i
$585$		0			0
$586$	−207.263			−0.353691
$587$	−465.123	−	124.629i	−0.792373	−	0.212316i	−0.160140	−	0.987094i	$-0.551195\pi$
$587$	−465.123	−	124.629i	−0.792373	−	0.212316i	−0.632233	+	0.774779i	$0.717861\pi$
$588$		0			0
$589$	−92.2295	−	53.2487i	−0.156587	−	0.0904053i
$590$	131.219	−	131.219i	0.222405	−	0.222405i
$591$		0			0
$592$	389.351	−	104.326i	0.657688	−	0.176227i
$593$	−389.671	−	389.671i	−0.657118	−	0.657118i	0.297579	−	0.954697i	$-0.403821\pi$
$593$	−389.671	−	389.671i	−0.657118	−	0.657118i	−0.954697	+	0.297579i	$0.903821\pi$
$594$		0			0
$595$	353.469	−	204.076i	0.594066	−	0.342984i
$596$	123.495	−	460.889i	0.207206	−	0.773304i
$597$		0			0
$598$	96.1000	+	96.1000i	0.160702	+	0.160702i
$599$	−808.596			−1.34991			−0.674955	−	0.737859i	$-0.735837\pi$
$599$	−808.596			−1.34991			−0.674955	+	0.737859i	$0.735837\pi$
$600$		0			0
$601$	221.344	+	383.379i	0.368293	+	0.637903i	0.989299	−	0.145904i	$-0.0466089\pi$
$601$	221.344	+	383.379i	0.368293	+	0.637903i	−0.621006	+	0.783806i	$0.713276\pi$
$602$	138.231	+	79.8076i	0.229619	+	0.132571i
$603$		0			0
$604$	−174.844	−	652.527i	−0.289477	−	1.08034i
$605$	−510.392	+	136.759i	−0.843623	+	0.226048i
$606$		0			0
$607$	471.398	−	816.485i	0.776603	−	1.34512i	−0.157286	−	0.987553i	$-0.550275\pi$
$607$	471.398	−	816.485i	0.776603	−	1.34512i	0.933889	−	0.357563i	$-0.116392\pi$
$608$	−123.916	+	71.5429i	−0.203809	+	0.117669i
$609$		0			0
$610$			49.4139i			0.0810065i
$611$	163.308	−	609.475i	0.267280	−	0.997504i
$612$		0			0
$613$	−973.161	−	260.758i	−1.58754	−	0.425380i	−0.646289	−	0.763093i	$-0.723680\pi$
$613$	−973.161	−	260.758i	−1.58754	−	0.425380i	−0.941249	+	0.337713i	$0.890347\pi$
$614$	95.2468	+	164.972i	0.155125	+	0.268685i
$615$		0			0
$616$	−272.287	+	272.287i	−0.442025	+	0.442025i
$617$	71.9115	+	268.378i	0.116550	+	0.434972i	0.999398	−	0.0346873i	$-0.0110435\pi$
$617$	71.9115	+	268.378i	0.116550	+	0.434972i	−0.882848	+	0.469659i	$0.844377\pi$
$618$		0			0
$619$	206.483	+	206.483i	0.333576	+	0.333576i	0.853943	−	0.520367i	$-0.174205\pi$
$619$	206.483	+	206.483i	0.333576	+	0.333576i	−0.520367	+	0.853943i	$0.674205\pi$
$620$	117.256	−	203.093i	0.189122	−	0.327569i
$621$		0			0
$622$	−9.57626	+	35.7391i	−0.0153959	+	0.0574583i
$623$		−	531.244i		−	0.852718i
$624$		0			0
$625$	223.140			0.357024
$626$	−197.158	−	52.8282i	−0.314948	−	0.0843902i
$627$		0			0
$628$	315.920	+	182.397i	0.503058	+	0.290441i
$629$	409.347	−	409.347i	0.650790	−	0.650790i
$630$		0			0
$631$	−428.813	+	114.900i	−0.679577	+	0.182092i	−0.582065	−	0.813142i	$-0.697755\pi$
$631$	−428.813	+	114.900i	−0.679577	+	0.182092i	−0.0975117	+	0.995234i	$0.531088\pi$
$632$	−177.580	−	177.580i	−0.280980	−	0.280980i
$633$		0			0
$634$	130.633	−	75.4212i	0.206046	−	0.118961i
$635$	−27.4608	+	102.485i	−0.0432454	+	0.161394i
$636$		0			0
$637$	155.192	+	89.6000i	0.243629	+	0.140659i
$638$	78.8231			0.123547
$639$		0			0
$640$	−207.120	−	358.742i	−0.323625	−	0.560535i
$641$	471.717	+	272.346i	0.735908	+	0.424877i	0.820580	−	0.571532i	$-0.193651\pi$
$641$	471.717	+	272.346i	0.735908	+	0.424877i	−0.0846714	+	0.996409i	$0.526984\pi$
$642$		0			0
$643$	100.073	+	373.478i	0.155635	+	0.580837i	0.999050	+	0.0435749i	$0.0138747\pi$
$643$	100.073	+	373.478i	0.155635	+	0.580837i	−0.843415	+	0.537262i	$0.819459\pi$
$644$	432.042	−	115.765i	0.670873	−	0.179760i
$645$		0			0
$646$	−30.1699	+	52.2558i	−0.0467026	+	0.0808913i
$647$	436.056	−	251.757i	0.673966	−	0.389114i	−0.123612	−	0.992331i	$-0.539448\pi$
$647$	436.056	−	251.757i	0.673966	−	0.389114i	0.797578	+	0.603216i	$0.206114\pi$
$648$		0			0
$649$		−	1560.32i		−	2.40420i
$650$	72.3083	−	19.3750i	0.111244	−	0.0298076i
$651$		0			0
$652$	456.363	+	122.282i	0.699943	+	0.187549i
$653$	15.5692	+	26.9667i	0.0238426	+	0.0412966i	0.877701	−	0.479210i	$-0.159077\pi$
$653$	15.5692	+	26.9667i	0.0238426	+	0.0412966i	−0.853858	+	0.520506i	$0.825743\pi$
$654$		0			0
$655$	7.85125	−	7.85125i	0.0119866	−	0.0119866i
$656$	−154.738	−	577.492i	−0.235882	−	0.880323i
$657$		0			0
$658$	105.426	+	105.426i	0.160221	+	0.160221i
$659$	379.488	−	657.293i	0.575855	−	0.997410i	−0.420093	−	0.907481i	$-0.638003\pi$
$659$	379.488	−	657.293i	0.575855	−	0.997410i	0.995948	−	0.0899292i	$-0.0286641\pi$
$660$		0			0
$661$	67.8083	−	253.064i	0.102584	−	0.382850i	−0.895475	−	0.445111i	$-0.853164\pi$
$661$	67.8083	−	253.064i	0.102584	−	0.382850i	0.998060	+	0.0622605i	$0.0198310\pi$
$662$		−	238.795i		−	0.360717i
$663$		0			0
$664$	−138.582			−0.208708
$665$	134.799	+	36.1192i	0.202705	+	0.0543146i
$666$		0			0
$667$	−164.275	−	94.8442i	−0.246289	−	0.142195i
$668$	−138.603	+	138.603i	−0.207489	+	0.207489i
$669$		0			0
$670$	75.2506	−	20.1633i	0.112314	−	0.0300945i
$671$	293.790	+	293.790i	0.437839	+	0.437839i
$672$		0			0
$673$	−272.210	+	157.160i	−0.404472	+	0.233522i	−0.688412	−	0.725320i	$-0.741692\pi$
$673$	−272.210	+	157.160i	−0.404472	+	0.233522i	0.283940	+	0.958842i	$0.408358\pi$
$674$	−19.3968	+	72.3897i	−0.0287786	+	0.107403i
$675$		0			0
$676$	546.217	−	315.358i	0.808013	−	0.466506i
$677$	547.384			0.808544			0.404272	−	0.914639i	$-0.367525\pi$
$677$	547.384			0.808544			0.404272	+	0.914639i	$0.367525\pi$
$678$		0			0
$679$	162.665	+	281.745i	0.239566	+	0.414941i
$680$	−238.400	−	137.640i	−0.350588	−	0.202412i
$681$		0			0
$682$	36.6410	+	136.746i	0.0537258	+	0.200508i
$683$	−252.954	+	67.7789i	−0.370358	+	0.0992371i	−0.439197	−	0.898391i	$-0.644737\pi$
$683$	−252.954	+	67.7789i	−0.370358	+	0.0992371i	0.0688393	+	0.997628i	$0.478070\pi$
$684$		0			0
$685$	−182.418	+	315.957i	−0.266303	+	0.461251i
$686$	−167.023	+	96.4308i	−0.243474	+	0.140570i
$687$		0			0
$688$			668.038i			0.970986i
$689$	−95.9749	−	166.233i	−0.139296	−	0.241268i
$690$		0			0
$691$	1062.75	+	284.764i	1.53799	+	0.412104i	0.925617	−	0.378462i	$-0.123547\pi$
$691$	1062.75	+	284.764i	1.53799	+	0.412104i	0.612377	+	0.790566i	$0.290214\pi$
$692$	256.119	+	443.611i	0.370114	+	0.641057i
$693$		0			0
$694$	178.321	−	178.321i	0.256946	−	0.256946i
$695$	31.2666	+	116.688i	0.0449879	+	0.167897i
$696$		0			0
$697$	−607.149	−	607.149i	−0.871089	−	0.871089i
$698$	−3.04036	+	5.26606i	−0.00435582	+	0.00754450i
$699$		0			0
$700$	63.7654	−	237.976i	0.0910934	−	0.339965i
$701$			638.323i			0.910589i	0.890341	+	0.455295i	$0.150466\pi$
$701$			638.323i			0.910589i	−0.890341	+	0.455295i	$0.849534\pi$
$702$		0			0
$703$	197.937			0.281561
$704$	−621.611	−	166.560i	−0.882971	−	0.236591i
$705$		0			0
$706$	128.171	+	73.9993i	0.181545	+	0.104815i
$707$	−671.363	+	671.363i	−0.949594	+	0.949594i
$708$		0			0
$709$	−625.185	+	167.518i	−0.881784	+	0.236273i	−0.671177	−	0.741297i	$-0.734211\pi$
$709$	−625.185	+	167.518i	−0.881784	+	0.236273i	−0.210608	+	0.977571i	$0.567544\pi$
$710$	63.0770	+	63.0770i	0.0888408	+	0.0888408i
$711$		0			0
$712$	−310.298	+	179.151i	−0.435812	+	0.251616i
$713$	88.1769	−	329.081i	0.123670	−	0.461544i
$714$		0			0
$715$	−392.550	+	679.917i	−0.549021	+	0.950932i
$716$	3.89488			0.00543978
$717$		0			0
$718$	−33.7025	−	58.3744i	−0.0469394	−	0.0813015i
$719$	−1058.38	−	611.056i	−1.47202	−	0.849870i	−0.472512	−	0.881324i	$-0.656653\pi$
$719$	−1058.38	−	611.056i	−1.47202	−	0.849870i	−0.999505	+	0.0314543i	$0.989986\pi$
$720$		0			0
$721$	−120.984	−	451.517i	−0.167800	−	0.626237i
$722$	160.572	−	43.0251i	0.222399	−	0.0595915i
$723$		0			0
$724$	−43.0692	+	74.5981i	−0.0594879	+	0.103036i
$725$	−90.4852	+	52.2417i	−0.124807	+	0.0720575i
$726$		0			0
$727$			508.974i			0.700102i	0.936731	+	0.350051i	$0.113836\pi$
$727$			508.974i			0.700102i	−0.936731	+	0.350051i	$0.886164\pi$
$728$			308.767i			0.424130i
$729$		0			0
$730$	−50.7698	−	13.6037i	−0.0695477	−	0.0186353i
$731$	479.711	+	830.885i	0.656240	+	1.13664i
$732$		0			0
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.194689	−	0.980865i	$-0.437630\pi$
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.980865	−	0.194689i	$-0.0623699\pi$
$734$	−1.68138	−	6.27499i	−0.00229071	−	0.00854903i
$735$		0			0
$736$	−323.669	−	323.669i	−0.439768	−	0.439768i
$737$	327.520	−	567.282i	0.444397	−	0.769718i
$738$		0			0
$739$	40.4242	−	150.865i	0.0547013	−	0.204148i	−0.933167	−	0.359444i	$-0.882966\pi$
$739$	40.4242	−	150.865i	0.0547013	−	0.204148i	0.987868	+	0.155296i	$0.0496331\pi$
$740$			435.865i			0.589007i
$741$		0			0
$742$	45.3562			0.0611270
$743$	369.252	+	98.9409i	0.496975	+	0.133164i	0.498596	−	0.866835i	$-0.333849\pi$
$743$	369.252	+	98.9409i	0.496975	+	0.133164i	−0.00162070	+	0.999999i	$0.500516\pi$
$744$		0			0
$745$	412.441	+	238.123i	0.553613	+	0.319628i
$746$	113.935	−	113.935i	0.152728	−	0.152728i
$747$		0			0
$748$	−1079.13	+	289.153i	−1.44269	+	0.386568i
$749$	−400.038	−	400.038i	−0.534097	−	0.534097i
$750$		0			0
$751$	−906.415	+	523.319i	−1.20694	+	0.696830i	−0.962091	−	0.272730i	$-0.912073\pi$
$751$	−906.415	+	523.319i	−1.20694	+	0.696830i	−0.244854	+	0.969560i	$0.578740\pi$
$752$	−161.504	+	602.743i	−0.214767	+	0.801520i
$753$		0			0
$754$	44.6917	−	44.6917i	0.0592728	−	0.0592728i
$755$	674.270			0.893073
$756$		0			0
$757$	188.415	+	326.345i	0.248897	+	0.431103i	0.963220	−	0.268713i	$-0.0865985\pi$
$757$	188.415	+	326.345i	0.248897	+	0.431103i	−0.714323	+	0.699816i	$0.753265\pi$
$758$	176.293	+	101.783i	0.232576	+	0.134278i
$759$		0			0
$760$	−24.3609	−	90.9160i	−0.0320538	−	0.119626i
$761$	742.044	−	198.830i	0.975091	−	0.261275i	0.264115	−	0.964491i	$-0.414920\pi$
$761$	742.044	−	198.830i	0.975091	−	0.261275i	0.710976	+	0.703216i	$0.248253\pi$
$762$		0			0
$763$	−218.119	+	377.794i	−0.285871	+	0.495142i
$764$	−950.235	+	548.619i	−1.24376	+	0.718087i
$765$		0			0
$766$		−	382.123i		−	0.498855i
$767$	−884.683	−	884.683i	−1.15343	−	1.15343i
$768$		0			0
$769$	−65.7006	−	17.6044i	−0.0854364	−	0.0228926i	0.215848	−	0.976427i	$-0.430749\pi$
$769$	−65.7006	−	17.6044i	−0.0854364	−	0.0228926i	−0.301284	+	0.953534i	$0.597415\pi$
$770$	−92.7564	−	160.659i	−0.120463	−	0.208648i
$771$		0			0
$772$	−872.288	+	872.288i	−1.12991	+	1.12991i
$773$	238.681	+	890.771i	0.308773	+	1.15236i	0.929649	+	0.368447i	$0.120110\pi$
$773$	238.681	+	890.771i	0.308773	+	1.15236i	−0.620876	+	0.783909i	$0.713223\pi$
$774$		0			0
$775$	−132.694	−	132.694i	−0.171218	−	0.171218i
$776$	109.711	−	190.025i	0.141380	−	0.244877i
$777$		0			0
$778$	46.1513	−	172.239i	0.0593205	−	0.221387i
$779$		−	293.583i		−	0.376872i
$780$		0			0
$781$	750.046			0.960366
$782$	−186.452	−	49.9596i	−0.238430	−	0.0638870i
$783$		0			0
$784$	−153.477	−	88.6103i	−0.195762	−	0.113023i
$785$	−257.461	+	257.461i	−0.327976	+	0.327976i
$786$		0			0
$787$	1188.62	−	318.489i	1.51031	−	0.404687i	0.593774	−	0.804632i	$-0.297637\pi$
$787$	1188.62	−	318.489i	1.51031	−	0.404687i	0.916540	+	0.399944i	$0.130970\pi$
$788$	232.531	+	232.531i	0.295090	+	0.295090i
$789$		0			0
$790$	104.778	−	60.4936i	0.132630	−	0.0765742i
$791$	−221.140	+	825.305i	−0.279570	+	1.04337i
$792$		0			0
$793$	333.150			0.420114
$794$	−363.565			−0.457891
$795$		0			0
$796$	−375.892	−	651.063i	−0.472226	−	0.817919i
$797$	22.0615	+	12.7372i	0.0276807	+	0.0159814i	0.513776	−	0.857924i	$-0.328246\pi$
$797$	22.0615	+	12.7372i	0.0276807	+	0.0159814i	−0.486096	+	0.873906i	$0.661579\pi$
$798$		0			0
$799$	231.949	+	865.647i	0.290300	+	1.08341i
$800$	−243.538	+	65.2558i	−0.304422	+	0.0815697i
$801$		0			0
$802$	−146.833	+	254.323i	−0.183084	+	0.317110i
$803$	−382.732	+	220.970i	−0.476628	+	0.275181i
$804$		0			0
$805$			446.438i			0.554582i
$806$	98.3083	+	56.7583i	0.121971	+	0.0704198i
$807$		0			0
$808$	618.544	+	165.738i	0.765525	+	0.205122i
$809$	−351.463	−	608.752i	−0.434442	−	0.752475i	0.562808	−	0.826588i	$-0.309721\pi$
$809$	−351.463	−	608.752i	−0.434442	−	0.752475i	−0.997250	+	0.0741123i	$0.976388\pi$
$810$		0			0
$811$	506.292	−	506.292i	0.624282	−	0.624282i	−0.322342	−	0.946623i	$-0.604470\pi$
$811$	506.292	−	506.292i	0.624282	−	0.624282i	0.946623	+	0.322342i	$0.104470\pi$
$812$	−53.8372	−	200.923i	−0.0663019	−	0.247442i
$813$		0			0
$814$	−186.056	−	186.056i	−0.228570	−	0.228570i
$815$	−235.785	+	408.391i	−0.289306	+	0.501093i
$816$		0			0
$817$	−84.9038	+	316.865i	−0.103921	+	0.387840i
$818$			52.6424i			0.0643550i
$819$		0			0
$820$	646.482			0.788393
$821$	1090.79	+	292.276i	1.32861	+	0.356000i	0.852197	−	0.523220i	$-0.175270\pi$
$821$	1090.79	+	292.276i	1.32861	+	0.356000i	0.476414	+	0.879221i	$0.341936\pi$
$822$		0			0
$823$	−449.858	−	259.726i	−0.546607	−	0.315584i	0.201145	−	0.979561i	$-0.435534\pi$
$823$	−449.858	−	259.726i	−0.546607	−	0.315584i	−0.747752	+	0.663978i	$0.768867\pi$
$824$	−222.931	+	222.931i	−0.270547	+	0.270547i
$825$		0			0
$826$	285.559	−	76.5153i	0.345713	−	0.0926335i
$827$	571.769	+	571.769i	0.691377	+	0.691377i	0.962535	−	0.271158i	$-0.0874064\pi$
$827$	571.769	+	571.769i	0.691377	+	0.691377i	−0.271158	+	0.962535i	$0.587406\pi$
$828$		0			0
$829$	−848.094	+	489.647i	−1.02303	+	0.590648i	−0.914981	−	0.403497i	$-0.867795\pi$
$829$	−848.094	+	489.647i	−1.02303	+	0.590648i	−0.108052	+	0.994145i	$0.534461\pi$
$830$	17.2796	−	64.4885i	0.0208188	−	0.0776970i
$831$		0			0
$832$	−446.883	+	258.008i	−0.537119	+	0.310106i
$833$	−254.520			−0.305547
$834$		0			0
$835$	−97.8217	−	169.432i	−0.117152	−	0.202913i
$836$	−330.813	−	190.995i	−0.395709	−	0.228463i
$837$		0			0
$838$	86.3543	+	322.279i	0.103048	+	0.384581i
$839$	−513.757	+	137.661i	−0.612344	+	0.164077i	−0.551645	−	0.834079i	$-0.686000\pi$
$839$	−513.757	+	137.661i	−0.612344	+	0.164077i	−0.0606993	+	0.998156i	$0.519333\pi$
$840$		0			0
$841$	376.392	−	651.931i	0.447553	−	0.775185i
$842$	219.747	−	126.871i	0.260983	−	0.150678i
$843$		0			0
$844$			273.545i			0.324105i
$845$	162.933	+	608.075i	0.192820	+	0.719615i
$846$		0			0
$847$	−813.099	−	217.869i	−0.959975	−	0.257224i
$848$	94.9148	+	164.397i	0.111928	+	0.193865i
$849$		0			0
$850$	−75.1821	+	75.1821i	−0.0884495	+	0.0884495i
$851$	163.886	+	611.633i	0.192581	+	0.718722i
$852$		0			0
$853$	713.043	+	713.043i	0.835924	+	0.835924i	0.988320	−	0.152396i	$-0.0486989\pi$
$853$	713.043	+	713.043i	0.835924	+	0.835924i	−0.152396	+	0.988320i	$0.548699\pi$
$854$	−39.3604	+	68.1742i	−0.0460894	+	0.0798292i
$855$		0			0
$856$	−98.7569	+	368.566i	−0.115370	+	0.430568i
$857$		−	311.663i		−	0.363667i	−0.983329	−	0.181834i	$-0.941797\pi$
$857$		−	311.663i		−	0.363667i	0.983329	−	0.181834i	$-0.0582032\pi$
$858$		0			0
$859$	−1475.02			−1.71714			−0.858568	−	0.512700i	$-0.828645\pi$
$859$	−1475.02			−1.71714			−0.858568	+	0.512700i	$0.828645\pi$
$860$	−697.750	−	186.962i	−0.811337	−	0.217397i
$861$		0			0
$862$	−47.1985	−	27.2501i	−0.0547547	−	0.0316126i
$863$	700.396	−	700.396i	0.811583	−	0.811583i	−0.173288	−	0.984871i	$-0.555439\pi$
$863$	700.396	−	700.396i	0.811583	−	0.811583i	0.984871	+	0.173288i	$0.0554392\pi$
$864$		0			0
$865$	−493.850	+	132.327i	−0.570925	+	0.152979i
$866$	252.276	+	252.276i	0.291312	+	0.291312i
$867$		0			0
$868$	323.545	−	186.799i	0.372747	−	0.215206i
$869$	263.292	−	982.620i	0.302983	−	1.13075i
$870$		0			0
$871$	−135.942	−	507.342i	−0.156076	−	0.582482i
$872$	294.224			0.337413
$873$		0			0
$874$	−33.0000	−	57.1577i	−0.0377574	−	0.0653978i
$875$	691.550	+	399.267i	0.790343	+	0.456305i
$876$		0			0
$877$	−35.4498	−	132.301i	−0.0404217	−	0.150856i	0.942765	−	0.333457i	$-0.108215\pi$
$877$	−35.4498	−	132.301i	−0.0404217	−	0.150856i	−0.983187	+	0.182601i	$0.941548\pi$
$878$	45.0666	−	12.0756i	0.0513287	−	0.0137535i
$879$		0			0
$880$	388.214	−	672.406i	0.441152	−	0.764098i
$881$	−383.677	+	221.516i	−0.435502	+	0.251437i	−0.701688	−	0.712485i	$-0.747570\pi$
$881$	−383.677	+	221.516i	−0.435502	+	0.251437i	0.266186	+	0.963922i	$0.414236\pi$
$882$		0			0
$883$		−	1305.20i		−	1.47814i	−0.673630	−	0.739069i	$-0.735266\pi$
$883$		−	1305.20i		−	1.47814i	0.673630	−	0.739069i	$-0.264734\pi$
$884$	−447.908	+	775.800i	−0.506684	+	0.877602i
$885$		0			0
$886$	−321.138	−	86.0488i	−0.362459	−	0.0971205i
$887$	−861.377	−	1491.95i	−0.971113	−	1.68202i	−0.692209	−	0.721697i	$-0.743362\pi$
$887$	−861.377	−	1491.95i	−0.971113	−	1.68202i	−0.278904	−	0.960319i	$-0.589971\pi$
$888$		0			0
$889$	−119.520	+	119.520i	−0.134444	+	0.134444i
$890$	−44.6762	−	166.734i	−0.0501980	−	0.187342i
$891$		0			0
$892$	1004.12	+	1004.12i	1.12569	+	1.12569i
$893$	−153.210	+	265.368i	−0.171568	+	0.297165i
$894$		0			0
$895$	−1.00617	+	3.75506i	−0.00112421	+	0.00419560i
$896$		−	659.920i		−	0.736518i
$897$		0			0
$898$	−12.1117			−0.0134874
$899$	−153.040	−	41.0070i	−0.170234	−	0.0456141i
$900$		0			0
$901$	236.104	+	136.315i	0.262047	+	0.151293i
$902$	−275.962	+	275.962i	−0.305944	+	0.305944i
$903$		0			0
$904$	556.633	−	149.149i	0.615745	−	0.164988i
$905$	−60.7940	−	60.7940i	−0.0671757	−	0.0671757i
$906$		0			0
$907$	758.800	−	438.093i	0.836604	−	0.483014i	−0.0195043	−	0.999810i	$-0.506209\pi$
$907$	758.800	−	438.093i	0.836604	−	0.483014i	0.856109	+	0.516796i	$0.172875\pi$
$908$	404.107	−	1508.15i	0.445052	−	1.66096i
$909$		0			0
$910$	−143.683	−	38.4998i	−0.157894	−	0.0423075i
$911$	1103.35			1.21114			0.605569	−	0.795793i	$-0.292946\pi$
$911$	1103.35			1.21114			0.605569	+	0.795793i	$0.292946\pi$
$912$		0			0
$913$	−280.679	−	486.151i	−0.307426	−	0.532477i
$914$	106.139	+	61.2795i	0.116126	+	0.0670454i
$915$		0			0
$916$	98.7199	+	368.428i	0.107773	+	0.402213i
$917$	17.0859	−	4.57815i	0.0186324	−	0.00499253i
$918$		0			0
$919$	328.160	−	568.389i	0.357083	−	0.618486i	−0.630389	−	0.776279i	$-0.717105\pi$
$919$	328.160	−	568.389i	0.357083	−	0.618486i	0.987472	+	0.157793i	$0.0504379\pi$
$920$	260.763	−	150.552i	0.283439	−	0.163643i
$921$		0			0
$922$			25.2065i			0.0273389i
$923$	425.267	−	425.267i	0.460744	−	0.460744i
$924$		0			0
$925$	336.897	+	90.2712i	0.364213	+	0.0975905i
$926$	−190.769	−	330.422i	−0.206014	−	0.356827i
$927$		0			0
$928$	−150.524	+	150.524i	−0.162202	+	0.162202i
$929$	−219.574	−	819.460i	−0.236355	−	0.882088i	−0.977533	−	0.210780i	$-0.932399\pi$
$929$	−219.574	−	819.460i	−0.236355	−	0.882088i	0.741179	−	0.671308i	$-0.234267\pi$
$930$		0			0
$931$	−61.5359	−	61.5359i	−0.0660966	−	0.0660966i
$932$	−478.808	+	829.319i	−0.513742	+	0.889827i
$933$		0			0
$934$	−18.9461	+	70.7077i	−0.0202849	+	0.0757041i
$935$		−	1115.09i		−	1.19261i
$936$		0			0
$937$	842.615			0.899269			0.449635	−	0.893213i	$-0.351554\pi$
$937$	842.615			0.899269			0.449635	+	0.893213i	$0.351554\pi$
$938$	119.881	+	32.1220i	0.127805	+	0.0342452i
$939$		0			0
$940$	−584.351	−	337.375i	−0.621650	−	0.358910i
$941$	471.659	−	471.659i	0.501232	−	0.501232i	−0.410589	−	0.911821i	$-0.634677\pi$
$941$	471.659	−	471.659i	0.501232	−	0.501232i	0.911821	+	0.410589i	$0.134677\pi$
$942$		0			0
$943$	907.183	−	243.079i	0.962018	−	0.257772i
$944$	874.911	+	874.911i	0.926813	+	0.926813i
$945$		0			0
$946$	377.654	−	218.038i	0.399211	−	0.230485i
$947$	131.110	−	489.308i	0.138447	−	0.516693i	−0.861512	−	0.507737i	$-0.830482\pi$
$947$	131.110	−	489.308i	0.138447	−	0.516693i	0.999960	−	0.00895652i	$-0.00285099\pi$
$948$		0			0
$949$	−91.7168	+	342.292i	−0.0966457	+	0.360687i
$950$	−36.3538			−0.0382672
$951$		0			0
$952$	−219.273	−	379.792i	−0.230329	−	0.398941i
$953$	770.092	+	444.613i	0.808071	+	0.466540i	0.846286	−	0.532729i	$-0.178834\pi$
$953$	770.092	+	444.613i	0.808071	+	0.466540i	−0.0382143	+	0.999270i	$0.512167\pi$
$954$		0			0
$955$	−283.450	−	1057.85i	−0.296806	−	1.10769i
$956$	200.583	−	53.7461i	0.209815	−	0.0562198i
$957$		0			0
$958$	−193.783	+	335.642i	−0.202278	+	0.350356i
$959$	−503.347	+	290.608i	−0.524867	+	0.303032i
$960$		0			0
$961$			676.436i			0.703888i
$962$	−210.983			−0.219317
$963$		0			0
$964$	−870.879	−	233.351i	−0.903401	−	0.242066i
$965$	−615.636	−	1066.31i	−0.637964	−	1.10499i
$966$		0			0
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	−0.877326	−	0.479894i	$-0.840675\pi$
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	0.479894	+	0.877326i	$0.340675\pi$
$968$	146.943	+	548.401i	0.151801	+	0.566529i
$969$		0			0
$970$	74.7475	+	74.7475i	0.0770593	+	0.0770593i
$971$	−121.863	+	211.074i	−0.125503	+	0.217378i	−0.921929	−	0.387358i	$-0.873388\pi$
$971$	−121.863	+	211.074i	−0.125503	+	0.217378i	0.796426	+	0.604735i	$0.206721\pi$
$972$		0			0
$973$	−49.8104	+	185.895i	−0.0511926	+	0.191053i
$974$		−	125.874i		−	0.129234i
$975$		0			0
$976$	−329.470			−0.337572
$977$	1110.01	+	297.426i	1.13614	+	0.304428i	0.777398	−	0.629009i	$-0.216539\pi$
$977$	1110.01	+	297.426i	1.13614	+	0.304428i	0.358742	+	0.933437i	$0.383206\pi$
$978$		0			0
$979$	−1256.94	−	725.692i	−1.28390	−	0.741259i
$980$	135.504	−	135.504i	0.138270	−	0.138270i
$981$		0			0
$982$	42.3308	−	11.3425i	0.0431067	−	0.0115504i
$983$	774.213	+	774.213i	0.787602	+	0.787602i	0.981101	−	0.193499i	$-0.0619835\pi$
$983$	774.213	+	774.213i	0.787602	+	0.787602i	−0.193499	+	0.981101i	$0.561984\pi$
$984$		0			0
$985$	−284.253	+	164.114i	−0.288582	+	0.166613i
$986$	−23.2339	+	86.7102i	−0.0235638	+	0.0879414i
$987$		0			0
$988$	−295.858	+	79.2750i	−0.299452	+	0.0802378i
$989$	−1049.42			−1.06109
$990$		0			0
$991$	391.733	+	678.501i	0.395290	+	0.684663i	0.993138	−	0.116947i	$-0.0373107\pi$
$991$	391.733	+	678.501i	0.395290	+	0.684663i	−0.597848	+	0.801609i	$0.703977\pi$
$992$	−331.107	−	191.165i	−0.333777	−	0.192706i
$993$		0			0
$994$	36.7808	+	137.268i	0.0370029	+	0.138097i
$995$	724.795	−	194.208i	0.728438	−	0.195184i
$996$		0			0
$997$	−250.817	+	434.428i	−0.251572	+	0.435735i	−0.963959	−	0.266052i	$-0.914281\pi$
$997$	−250.817	+	434.428i	−0.251572	+	0.435735i	0.712387	+	0.701787i	$0.247614\pi$
$998$	−85.2046	+	49.1929i	−0.0853753	+	0.0492915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.bd.b.28.1		4
3.2	odd	2		13.3.f.a.2.1	✓	4
12.11	even	2		208.3.bd.d.145.1		4
13.7	odd	12	inner	117.3.bd.b.46.1		4
15.2	even	4		325.3.w.b.249.1		4
15.8	even	4		325.3.w.a.249.1		4
15.14	odd	2		325.3.t.a.301.1		4
39.2	even	12		169.3.d.c.99.1		4
39.5	even	4		169.3.f.a.89.1		4
39.8	even	4		169.3.f.c.89.1		4
39.11	even	12		169.3.d.a.99.2		4
39.17	odd	6		169.3.f.a.19.1		4
39.20	even	12		13.3.f.a.7.1	yes	4
39.23	odd	6		169.3.d.c.70.1		4
39.29	odd	6		169.3.d.a.70.2		4
39.32	even	12		169.3.f.b.150.1		4
39.35	odd	6		169.3.f.c.19.1		4
39.38	odd	2		169.3.f.b.80.1		4
156.59	odd	12		208.3.bd.d.33.1		4
195.59	even	12		325.3.t.a.176.1		4
195.98	odd	12		325.3.w.b.124.1		4
195.137	odd	12		325.3.w.a.124.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.2.1	✓	4	3.2	odd	2
13.3.f.a.7.1	yes	4	39.20	even	12
117.3.bd.b.28.1		4	1.1	even	1	trivial
117.3.bd.b.46.1		4	13.7	odd	12	inner
169.3.d.a.70.2		4	39.29	odd	6
169.3.d.a.99.2		4	39.11	even	12
169.3.d.c.70.1		4	39.23	odd	6
169.3.d.c.99.1		4	39.2	even	12
169.3.f.a.19.1		4	39.17	odd	6
169.3.f.a.89.1		4	39.5	even	4
169.3.f.b.80.1		4	39.38	odd	2
169.3.f.b.150.1		4	39.32	even	12
169.3.f.c.19.1		4	39.35	odd	6
169.3.f.c.89.1		4	39.8	even	4
208.3.bd.d.33.1		4	156.59	odd	12
208.3.bd.d.145.1		4	12.11	even	2
325.3.t.a.176.1		4	195.59	even	12
325.3.t.a.301.1		4	15.14	odd	2
325.3.w.a.124.1		4	195.137	odd	12
325.3.w.a.249.1		4	15.8	even	4
325.3.w.b.124.1		4	195.98	odd	12
325.3.w.b.249.1		4	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.133975i) q^{2} +(-3.23205 - 1.86603i) q^{4} +(2.63397 - 2.63397i) q^{5} +(5.73205 - 1.53590i) q^{7} +(-2.83013 - 2.83013i) q^{8} +(1.66987 - 0.964102i) q^{10} +(4.19615 - 15.6603i) q^{11} +(-6.50000 - 11.2583i) q^{13} +3.07180 q^{14} +(6.42820 + 11.1340i) q^{16} +(15.9904 + 9.23205i) q^{17} +(1.63397 + 6.09808i) q^{19} +(-13.4282 + 3.59808i) q^{20} +(4.19615 - 7.26795i) q^{22} +(-17.4904 + 10.0981i) q^{23} +11.1244i q^{25} +(-1.74167 - 6.50000i) q^{26} +(-21.3923 - 5.73205i) q^{28} +(4.69615 + 8.13397i) q^{29} +(-11.9282 + 11.9282i) q^{31} +(5.86603 + 21.8923i) q^{32} +(6.75833 + 6.75833i) q^{34} +(11.0526 - 19.1436i) q^{35} +(8.11474 - 30.2846i) q^{37} +3.26795i q^{38} -14.9090 q^{40} +(-44.9186 - 12.0359i) q^{41} +(45.0000 + 25.9808i) q^{43} +(-42.7846 + 42.7846i) q^{44} +(-10.0981 + 2.70577i) q^{46} +(34.3205 + 34.3205i) q^{47} +(-11.9378 + 6.89230i) q^{49} +(-1.49038 + 5.56218i) q^{50} +48.5167i q^{52} +14.7654 q^{53} +(-30.1962 - 52.3013i) q^{55} +(-20.5692 - 11.8756i) q^{56} +(1.25833 + 4.69615i) q^{58} +(92.9615 - 24.9090i) q^{59} +(-12.8135 + 22.1936i) q^{61} +(-7.56218 + 4.36603i) q^{62} -39.6936i q^{64} +(-46.7750 - 12.5333i) q^{65} +(39.0263 + 10.4571i) q^{67} +(-34.4545 - 59.6769i) q^{68} +(8.09103 - 8.09103i) q^{70} +(11.9737 + 44.6865i) q^{71} +(-19.2750 - 19.2750i) q^{73} +(8.11474 - 14.0551i) q^{74} +(6.09808 - 22.7583i) q^{76} -96.2102i q^{77} +62.7461 q^{79} +(46.2583 + 12.3949i) q^{80} +(-20.8468 - 12.0359i) q^{82} +(24.4833 - 24.4833i) q^{83} +(66.4352 - 17.8013i) q^{85} +(19.0192 + 19.0192i) q^{86} +(-56.1962 + 32.4449i) q^{88} +(23.1699 - 86.4711i) q^{89} +(-54.5500 - 54.5500i) q^{91} +75.3731 q^{92} +(12.5622 + 21.7583i) q^{94} +(20.3660 + 11.7583i) q^{95} +(14.1891 + 52.9545i) q^{97} +(-6.89230 + 1.84679i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{4} + 14 q^{5} + 16 q^{7} + 6 q^{8} + 24 q^{10} - 4 q^{11} - 26 q^{13} + 40 q^{14} - 2 q^{16} + 12 q^{17} + 10 q^{19} - 26 q^{20} - 4 q^{22} - 18 q^{23} - 52 q^{26} - 44 q^{28} - 2 q^{29}+ \cdots + 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^4 + 14 * q^5 + 16 * q^7 + 6 * q^8 + 24 * q^10 - 4 * q^11 - 26 * q^13 + 40 * q^14 - 2 * q^16 + 12 * q^17 + 10 * q^19 - 26 * q^20 - 4 * q^22 - 18 * q^23 - 52 * q^26 - 44 * q^28 - 2 * q^29 - 20 * q^31 + 20 * q^32 - 18 * q^34 - 32 * q^35 - 68 * q^37 + 72 * q^40 - 100 * q^41 + 180 * q^43 - 88 * q^44 - 30 * q^46 + 68 * q^47 - 72 * q^49 + 46 * q^50 - 128 * q^53 - 100 * q^55 + 84 * q^56 - 40 * q^58 + 164 * q^59 - 124 * q^61 - 6 * q^62 - 52 * q^65 + 118 * q^67 - 72 * q^68 + 164 * q^70 + 86 * q^71 + 58 * q^73 - 68 * q^74 + 14 * q^76 - 40 * q^79 + 140 * q^80 + 24 * q^82 + 188 * q^83 + 96 * q^85 + 180 * q^86 - 204 * q^88 + 110 * q^89 + 52 * q^91 + 156 * q^92 + 26 * q^94 + 78 * q^95 + 178 * q^97 + 14 * q^98

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